City were booed off in their last home match and the supporters again voiced their disapproval at the end of this dull encounter.
City have struggled to find the sort of home form that can propel them into the play-offs and it was an all too familiar story again at Valley Parade as they failed to break down their determined and well organised visitors.
Colchester came with plan to frustrate the Bantams, playing with Chris Iwelumo as a lone striker with John White shielding the back four in a five-man midfield.
Bradford had plenty of possession but lacked the imagination to trouble the visitors in a forgettable opening 20 minutes.
Bradford's leading scorer Dean Windass did have the ball in the net, sliding in on Petta's cross-shot, but his celebrations were cut short by the assistant's flag.
With the visitors seemingly content to play for a draw, the onus was on Bradford to push forward but it took them 37 minutes to force United goalkeeper Aidan Davison a into a save.
Windass won his side a free-kick 25 yards out but Petta's curling effort was tipped wide by the former City stopper.
As the opening period meandered towards half-time, Windass spurned a glorious chance to give his side the lead. The ball ricochet to him inside the box and once he turned inside the last defender he only had the keeper beat, but Davison again kept his side level tipping around the post.
Mark Bower was next to miss a gilt-edged chance just after the restart when he was left unmarked from a corner but headed over from only five yards out.
Although Bradford had dominated possession it was Colchester who took the lead against the run of play on 62 minutes when City skipper David Wetherall was adjudged to have fouled Iwelumo 30 yards out.
Goalkeeper Russell Howarth took up a poor starting position well to his right and Greg Halford curled the ball into the opposite corner.
It looked as though Colchester had done enough to earn all three points as Bradford lacked the guile to break down the visitors.
But with just five minutes left City won a corner which was flicked on by Lee Crooks and Petta found himself free inside the box and guided his header into the bottom corner.
The equaliser breathed life into the Bantams as they pushed for a winner, and although Windass came close with a shot that flashed agonisingly wide, City had left it too late.